How do you find the tangent line?
For example, I was given a graph where a straight line crossed the x-axis at -0.25 and the y-axis at 1. Find f'(1/2). So to do this I would need to find the tangent line right? Im confused

the derivative gives you the formula for the slope. once you find the derivative and plug in the required x-value and that gives you your m in the equation of a line (y = mx + b), you can then use your m and a point the line passes through to get your tangent line. however, that is not the case here. you are required to find a slope, why would you find the tangent line. that's not what they asked for, and you don't need it to find the slope. (the tangent line for a straight line, at any point on the line, is itself, by the way). all you are doing is finding the slope of a line that passes through (-0.25, 0) and (0, 1). the slope (for all points on the straight line) is just given by , and you know what those components are, right?